TSTP Solution File: SET081-6 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET081-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:46:43 EDT 2022
% Result : Unsatisfiable 1.28s 1.65s
% Output : Refutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET081-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % DateTime : Mon Jul 11 09:45:04 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.71/1.11 *** allocated 10000 integers for termspace/termends
% 0.71/1.11 *** allocated 10000 integers for clauses
% 0.71/1.11 *** allocated 10000 integers for justifications
% 0.71/1.11 Bliksem 1.12
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Automatic Strategy Selection
% 0.71/1.11
% 0.71/1.11 Clauses:
% 0.71/1.11 [
% 0.71/1.11 [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y ) ],
% 0.71/1.11 [ member( 'not_subclass_element'( X, Y ), X ), subclass( X, Y ) ],
% 0.71/1.11 [ ~( member( 'not_subclass_element'( X, Y ), Y ) ), subclass( X, Y ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ subclass( X, 'universal_class' ) ],
% 0.71/1.11 [ ~( =( X, Y ) ), subclass( X, Y ) ],
% 0.71/1.11 [ ~( =( X, Y ) ), subclass( Y, X ) ],
% 0.71/1.11 [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ],
% 0.71/1.11 [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( X, Y
% 0.71/1.11 ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( X, 'unordered_pair'( Y, X
% 0.71/1.11 ) ) ],
% 0.71/1.11 [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ],
% 0.71/1.11 [ =( 'unordered_pair'( X, X ), singleton( X ) ) ],
% 0.71/1.11 [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X, singleton( Y
% 0.71/1.11 ) ) ), 'ordered_pair'( X, Y ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.11 X, Z ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T ) ) ), member(
% 0.71/1.11 Y, T ) ],
% 0.71/1.11 [ ~( member( X, Y ) ), ~( member( Z, T ) ), member( 'ordered_pair'( X, Z
% 0.71/1.11 ), 'cross_product'( Y, T ) ) ],
% 0.71/1.11 [ ~( member( X, 'cross_product'( Y, Z ) ) ), =( 'ordered_pair'( first( X
% 0.71/1.11 ), second( X ) ), X ) ],
% 0.71/1.11 [ subclass( 'element_relation', 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' ) ), member( X,
% 0.71/1.11 Y ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( 'universal_class'
% 0.71/1.11 , 'universal_class' ) ) ), ~( member( X, Y ) ), member( 'ordered_pair'( X
% 0.71/1.11 , Y ), 'element_relation' ) ],
% 0.71/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ],
% 0.71/1.11 [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ],
% 0.71/1.11 [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X, intersection( Y,
% 0.71/1.11 Z ) ) ],
% 0.71/1.11 [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( X, complement( Y ) ),
% 0.71/1.11 member( X, Y ) ],
% 0.71/1.11 [ =( complement( intersection( complement( X ), complement( Y ) ) ),
% 0.71/1.11 union( X, Y ) ) ],
% 0.71/1.11 [ =( intersection( complement( intersection( X, Y ) ), complement(
% 0.71/1.11 intersection( complement( X ), complement( Y ) ) ) ),
% 0.71/1.11 'symmetric_difference'( X, Y ) ) ],
% 0.71/1.11 [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict( X, Y, Z ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ =( intersection( 'cross_product'( X, Y ), Z ), restrict( Z, X, Y ) ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( =( restrict( X, singleton( Y ), 'universal_class' ), 'null_class' )
% 0.71/1.11 ), ~( member( Y, 'domain_of'( X ) ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), =( restrict( Y, singleton( X ),
% 0.71/1.11 'universal_class' ), 'null_class' ), member( X, 'domain_of'( Y ) ) ],
% 0.71/1.11 [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 0.71/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), rotate( T ) )
% 0.71/1.11 ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.71/1.11 member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ), 'cross_product'(
% 0.71/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.71/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X ),
% 0.71/1.11 Y ), rotate( T ) ) ],
% 0.71/1.11 [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 0.71/1.11 'universal_class', 'universal_class' ), 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), flip( T ) ) )
% 0.71/1.11 , member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ), T ) ), ~(
% 0.71/1.11 member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), 'cross_product'(
% 0.71/1.11 'cross_product'( 'universal_class', 'universal_class' ),
% 0.71/1.11 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ),
% 0.71/1.11 Z ), flip( T ) ) ],
% 0.71/1.11 [ =( 'domain_of'( flip( 'cross_product'( X, 'universal_class' ) ) ),
% 0.71/1.11 inverse( X ) ) ],
% 0.71/1.11 [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ],
% 0.71/1.11 [ =( first( 'not_subclass_element'( restrict( X, Y, singleton( Z ) ),
% 0.71/1.11 'null_class' ) ), domain( X, Y, Z ) ) ],
% 0.71/1.11 [ =( second( 'not_subclass_element'( restrict( X, singleton( Y ), Z ),
% 0.71/1.11 'null_class' ) ), range( X, Y, Z ) ) ],
% 0.71/1.11 [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ), image( X, Y ) )
% 0.71/1.11 ],
% 0.71/1.11 [ =( union( X, singleton( X ) ), successor( X ) ) ],
% 0.71/1.11 [ subclass( 'successor_relation', 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation' ) ), =(
% 0.71/1.11 successor( X ), Y ) ],
% 0.71/1.11 [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'( X, Y ),
% 0.71/1.11 'cross_product'( 'universal_class', 'universal_class' ) ) ), member(
% 0.71/1.11 'ordered_pair'( X, Y ), 'successor_relation' ) ],
% 0.71/1.11 [ ~( inductive( X ) ), member( 'null_class', X ) ],
% 0.71/1.11 [ ~( inductive( X ) ), subclass( image( 'successor_relation', X ), X ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 0.71/1.11 'successor_relation', X ), X ) ), inductive( X ) ],
% 0.71/1.11 [ inductive( omega ) ],
% 0.71/1.11 [ ~( inductive( X ) ), subclass( omega, X ) ],
% 0.71/1.11 [ member( omega, 'universal_class' ) ],
% 0.71/1.11 [ =( 'domain_of'( restrict( 'element_relation', 'universal_class', X ) )
% 0.71/1.11 , 'sum_class'( X ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( 'sum_class'( X ),
% 0.71/1.11 'universal_class' ) ],
% 0.71/1.11 [ =( complement( image( 'element_relation', complement( X ) ) ),
% 0.71/1.11 'power_class'( X ) ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), member( 'power_class'( X ),
% 0.71/1.11 'universal_class' ) ],
% 0.71/1.11 [ subclass( compose( X, Y ), 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ), member( Y,
% 0.71/1.11 image( Z, image( T, singleton( X ) ) ) ) ],
% 0.71/1.11 [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) ), ~( member(
% 0.71/1.11 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 0.71/1.11 ) ],
% 0.71/1.11 [ ~( 'single_valued_class'( X ) ), subclass( compose( X, inverse( X ) )
% 0.71/1.11 , 'identity_relation' ) ],
% 0.71/1.11 [ ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) ),
% 0.71/1.11 'single_valued_class'( X ) ],
% 0.71/1.11 [ ~( function( X ) ), subclass( X, 'cross_product'( 'universal_class',
% 0.71/1.11 'universal_class' ) ) ],
% 0.71/1.11 [ ~( function( X ) ), subclass( compose( X, inverse( X ) ),
% 0.71/1.11 'identity_relation' ) ],
% 0.71/1.11 [ ~( subclass( X, 'cross_product'( 'universal_class', 'universal_class'
% 0.71/1.11 ) ) ), ~( subclass( compose( X, inverse( X ) ), 'identity_relation' ) )
% 0.71/1.11 , function( X ) ],
% 0.71/1.11 [ ~( function( X ) ), ~( member( Y, 'universal_class' ) ), member( image(
% 0.71/1.11 X, Y ), 'universal_class' ) ],
% 0.71/1.11 [ =( X, 'null_class' ), member( regular( X ), X ) ],
% 0.71/1.11 [ =( X, 'null_class' ), =( intersection( X, regular( X ) ), 'null_class'
% 0.71/1.11 ) ],
% 0.71/1.11 [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X, Y ) ) ],
% 0.71/1.11 [ function( choice ) ],
% 0.71/1.11 [ ~( member( X, 'universal_class' ) ), =( X, 'null_class' ), member(
% 0.71/1.11 apply( choice, X ), X ) ],
% 0.71/1.11 [ ~( 'one_to_one'( X ) ), function( X ) ],
% 0.71/1.11 [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ],
% 0.71/1.11 [ ~( function( inverse( X ) ) ), ~( function( X ) ), 'one_to_one'( X ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ =( intersection( 'cross_product'( 'universal_class', 'universal_class'
% 0.71/1.11 ), intersection( 'cross_product'( 'universal_class', 'universal_class' )
% 0.71/1.11 , complement( compose( complement( 'element_relation' ), inverse(
% 0.71/1.11 'element_relation' ) ) ) ) ), 'subset_relation' ) ],
% 0.71/1.11 [ =( intersection( inverse( 'subset_relation' ), 'subset_relation' ),
% 0.71/1.11 'identity_relation' ) ],
% 0.71/1.11 [ =( complement( 'domain_of'( intersection( X, 'identity_relation' ) ) )
% 0.71/1.11 , diagonalise( X ) ) ],
% 0.71/1.11 [ =( intersection( 'domain_of'( X ), diagonalise( compose( inverse(
% 0.71/1.11 'element_relation' ), X ) ) ), cantor( X ) ) ],
% 0.71/1.11 [ ~( operation( X ) ), function( X ) ],
% 0.71/1.11 [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'( 'domain_of'( X )
% 0.71/1.11 ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ],
% 0.71/1.11 [ ~( operation( X ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.28/1.65 'domain_of'( X ) ) ) ],
% 1.28/1.65 [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'( 'domain_of'( X
% 1.28/1.65 ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) ) ), ~(
% 1.28/1.65 subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ), operation(
% 1.28/1.65 X ) ],
% 1.28/1.65 [ ~( compatible( X, Y, Z ) ), function( X ) ],
% 1.28/1.65 [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'( Y ) ),
% 1.28/1.65 'domain_of'( X ) ) ],
% 1.28/1.65 [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ), 'domain_of'(
% 1.28/1.65 'domain_of'( Z ) ) ) ],
% 1.28/1.65 [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y ) ), 'domain_of'(
% 1.28/1.65 X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( Z ) ) )
% 1.28/1.65 ), compatible( X, Y, Z ) ],
% 1.28/1.65 [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ],
% 1.28/1.65 [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ],
% 1.28/1.65 [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ],
% 1.28/1.65 [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'( T, U ),
% 1.28/1.65 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T ), apply(
% 1.28/1.65 X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ],
% 1.28/1.65 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.28/1.65 member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.28/1.65 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.28/1.65 , Y ) ],
% 1.28/1.65 [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible( Z, X, Y ) ),
% 1.28/1.65 ~( =( apply( Y, 'ordered_pair'( apply( Z, 'not_homomorphism1'( Z, X, Y )
% 1.28/1.65 ), apply( Z, 'not_homomorphism2'( Z, X, Y ) ) ) ), apply( Z, apply( X,
% 1.28/1.65 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ), 'not_homomorphism2'( Z, X
% 1.28/1.65 , Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ],
% 1.28/1.65 [ member( y, singleton( x ) ) ],
% 1.28/1.65 [ ~( =( y, x ) ) ]
% 1.28/1.65 ] .
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 percentage equality = 0.218579, percentage horn = 0.913978
% 1.28/1.65 This is a problem with some equality
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Options Used:
% 1.28/1.65
% 1.28/1.65 useres = 1
% 1.28/1.65 useparamod = 1
% 1.28/1.65 useeqrefl = 1
% 1.28/1.65 useeqfact = 1
% 1.28/1.65 usefactor = 1
% 1.28/1.65 usesimpsplitting = 0
% 1.28/1.65 usesimpdemod = 5
% 1.28/1.65 usesimpres = 3
% 1.28/1.65
% 1.28/1.65 resimpinuse = 1000
% 1.28/1.65 resimpclauses = 20000
% 1.28/1.65 substype = eqrewr
% 1.28/1.65 backwardsubs = 1
% 1.28/1.65 selectoldest = 5
% 1.28/1.65
% 1.28/1.65 litorderings [0] = split
% 1.28/1.65 litorderings [1] = extend the termordering, first sorting on arguments
% 1.28/1.65
% 1.28/1.65 termordering = kbo
% 1.28/1.65
% 1.28/1.65 litapriori = 0
% 1.28/1.65 termapriori = 1
% 1.28/1.65 litaposteriori = 0
% 1.28/1.65 termaposteriori = 0
% 1.28/1.65 demodaposteriori = 0
% 1.28/1.65 ordereqreflfact = 0
% 1.28/1.65
% 1.28/1.65 litselect = negord
% 1.28/1.65
% 1.28/1.65 maxweight = 15
% 1.28/1.65 maxdepth = 30000
% 1.28/1.65 maxlength = 115
% 1.28/1.65 maxnrvars = 195
% 1.28/1.65 excuselevel = 1
% 1.28/1.65 increasemaxweight = 1
% 1.28/1.65
% 1.28/1.65 maxselected = 10000000
% 1.28/1.65 maxnrclauses = 10000000
% 1.28/1.65
% 1.28/1.65 showgenerated = 0
% 1.28/1.65 showkept = 0
% 1.28/1.65 showselected = 0
% 1.28/1.65 showdeleted = 0
% 1.28/1.65 showresimp = 1
% 1.28/1.65 showstatus = 2000
% 1.28/1.65
% 1.28/1.65 prologoutput = 1
% 1.28/1.65 nrgoals = 5000000
% 1.28/1.65 totalproof = 1
% 1.28/1.65
% 1.28/1.65 Symbols occurring in the translation:
% 1.28/1.65
% 1.28/1.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.28/1.65 . [1, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.28/1.65 ! [4, 1] (w:0, o:31, a:1, s:1, b:0),
% 1.28/1.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.65 subclass [41, 2] (w:1, o:81, a:1, s:1, b:0),
% 1.28/1.65 member [43, 2] (w:1, o:82, a:1, s:1, b:0),
% 1.28/1.65 'not_subclass_element' [44, 2] (w:1, o:83, a:1, s:1, b:0),
% 1.28/1.65 'universal_class' [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.28/1.65 'unordered_pair' [46, 2] (w:1, o:84, a:1, s:1, b:0),
% 1.28/1.65 singleton [47, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.28/1.65 'ordered_pair' [48, 2] (w:1, o:85, a:1, s:1, b:0),
% 1.28/1.65 'cross_product' [50, 2] (w:1, o:86, a:1, s:1, b:0),
% 1.28/1.65 first [52, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.28/1.65 second [53, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.28/1.65 'element_relation' [54, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.28/1.65 intersection [55, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.28/1.65 complement [56, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.28/1.65 union [57, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.28/1.65 'symmetric_difference' [58, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.28/1.65 restrict [60, 3] (w:1, o:93, a:1, s:1, b:0),
% 1.28/1.65 'null_class' [61, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.28/1.65 'domain_of' [62, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.28/1.65 rotate [63, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.28/1.65 flip [65, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.28/1.65 inverse [66, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.28/1.65 'range_of' [67, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.28/1.65 domain [68, 3] (w:1, o:95, a:1, s:1, b:0),
% 1.28/1.65 range [69, 3] (w:1, o:96, a:1, s:1, b:0),
% 1.28/1.65 image [70, 2] (w:1, o:87, a:1, s:1, b:0),
% 1.28/1.65 successor [71, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.28/1.65 'successor_relation' [72, 0] (w:1, o:6, a:1, s:1, b:0),
% 1.28/1.65 inductive [73, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.28/1.65 omega [74, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.28/1.65 'sum_class' [75, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.28/1.65 'power_class' [76, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.28/1.65 compose [78, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.28/1.65 'single_valued_class' [79, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.28/1.65 'identity_relation' [80, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.28/1.65 function [82, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.28/1.65 regular [83, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.28/1.65 apply [84, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.28/1.65 choice [85, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.28/1.65 'one_to_one' [86, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.28/1.65 'subset_relation' [87, 0] (w:1, o:5, a:1, s:1, b:0),
% 1.28/1.65 diagonalise [88, 1] (w:1, o:55, a:1, s:1, b:0),
% 1.28/1.65 cantor [89, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.28/1.65 operation [90, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.28/1.65 compatible [94, 3] (w:1, o:94, a:1, s:1, b:0),
% 1.28/1.65 homomorphism [95, 3] (w:1, o:97, a:1, s:1, b:0),
% 1.28/1.65 'not_homomorphism1' [96, 3] (w:1, o:98, a:1, s:1, b:0),
% 1.28/1.65 'not_homomorphism2' [97, 3] (w:1, o:99, a:1, s:1, b:0),
% 1.28/1.65 y [98, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.28/1.65 x [99, 0] (w:1, o:29, a:1, s:1, b:0).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Starting Search:
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Intermediate Status:
% 1.28/1.65 Generated: 5137
% 1.28/1.65 Kept: 2006
% 1.28/1.65 Inuse: 109
% 1.28/1.65 Deleted: 7
% 1.28/1.65 Deletedinuse: 2
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Intermediate Status:
% 1.28/1.65 Generated: 9827
% 1.28/1.65 Kept: 4020
% 1.28/1.65 Inuse: 184
% 1.28/1.65 Deleted: 16
% 1.28/1.65 Deletedinuse: 6
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Intermediate Status:
% 1.28/1.65 Generated: 13714
% 1.28/1.65 Kept: 6051
% 1.28/1.65 Inuse: 235
% 1.28/1.65 Deleted: 18
% 1.28/1.65 Deletedinuse: 6
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Intermediate Status:
% 1.28/1.65 Generated: 18755
% 1.28/1.65 Kept: 8213
% 1.28/1.65 Inuse: 287
% 1.28/1.65 Deleted: 61
% 1.28/1.65 Deletedinuse: 47
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65 Resimplifying inuse:
% 1.28/1.65 Done
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Bliksems!, er is een bewijs:
% 1.28/1.65 % SZS status Unsatisfiable
% 1.28/1.65 % SZS output start Refutation
% 1.28/1.65
% 1.28/1.65 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 1.28/1.65 ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 90, [ member( y, singleton( x ) ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 91, [ ~( =( y, x ) ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 93, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 122, [ =( X, Y ), ~( =( Y, X ) ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 165, [ member( X, singleton( x ) ), ~( =( X, y ) ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 170, [ ~( =( X, x ) ), ~( =( X, y ) ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 10101, [ ~( =( X, y ) ) ] )
% 1.28/1.65 .
% 1.28/1.65 clause( 11198, [] )
% 1.28/1.65 .
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 % SZS output end Refutation
% 1.28/1.65 found a proof!
% 1.28/1.65
% 1.28/1.65 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.28/1.65
% 1.28/1.65 initialclauses(
% 1.28/1.65 [ clause( 11200, [ ~( subclass( X, Y ) ), ~( member( Z, X ) ), member( Z, Y
% 1.28/1.65 ) ] )
% 1.28/1.65 , clause( 11201, [ member( 'not_subclass_element'( X, Y ), X ), subclass( X
% 1.28/1.65 , Y ) ] )
% 1.28/1.65 , clause( 11202, [ ~( member( 'not_subclass_element'( X, Y ), Y ) ),
% 1.28/1.65 subclass( X, Y ) ] )
% 1.28/1.65 , clause( 11203, [ subclass( X, 'universal_class' ) ] )
% 1.28/1.65 , clause( 11204, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.28/1.65 , clause( 11205, [ ~( =( X, Y ) ), subclass( Y, X ) ] )
% 1.28/1.65 , clause( 11206, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.28/1.65 ] )
% 1.28/1.65 , clause( 11207, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.28/1.65 =( X, Z ) ] )
% 1.28/1.65 , clause( 11208, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.28/1.65 'unordered_pair'( X, Y ) ) ] )
% 1.28/1.65 , clause( 11209, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.28/1.65 'unordered_pair'( Y, X ) ) ] )
% 1.28/1.65 , clause( 11210, [ member( 'unordered_pair'( X, Y ), 'universal_class' ) ]
% 1.28/1.65 )
% 1.28/1.65 , clause( 11211, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.28/1.65 , clause( 11212, [ =( 'unordered_pair'( singleton( X ), 'unordered_pair'( X
% 1.28/1.65 , singleton( Y ) ) ), 'ordered_pair'( X, Y ) ) ] )
% 1.28/1.65 , clause( 11213, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.28/1.65 ) ) ), member( X, Z ) ] )
% 1.28/1.65 , clause( 11214, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'( Z, T
% 1.28/1.65 ) ) ), member( Y, T ) ] )
% 1.28/1.65 , clause( 11215, [ ~( member( X, Y ) ), ~( member( Z, T ) ), member(
% 1.28/1.65 'ordered_pair'( X, Z ), 'cross_product'( Y, T ) ) ] )
% 1.28/1.65 , clause( 11216, [ ~( member( X, 'cross_product'( Y, Z ) ) ), =(
% 1.28/1.65 'ordered_pair'( first( X ), second( X ) ), X ) ] )
% 1.28/1.65 , clause( 11217, [ subclass( 'element_relation', 'cross_product'(
% 1.28/1.65 'universal_class', 'universal_class' ) ) ] )
% 1.28/1.65 , clause( 11218, [ ~( member( 'ordered_pair'( X, Y ), 'element_relation' )
% 1.28/1.65 ), member( X, Y ) ] )
% 1.28/1.65 , clause( 11219, [ ~( member( 'ordered_pair'( X, Y ), 'cross_product'(
% 1.28/1.65 'universal_class', 'universal_class' ) ) ), ~( member( X, Y ) ), member(
% 1.28/1.65 'ordered_pair'( X, Y ), 'element_relation' ) ] )
% 1.28/1.65 , clause( 11220, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Y ) ]
% 1.28/1.65 )
% 1.28/1.65 , clause( 11221, [ ~( member( X, intersection( Y, Z ) ) ), member( X, Z ) ]
% 1.28/1.65 )
% 1.28/1.65 , clause( 11222, [ ~( member( X, Y ) ), ~( member( X, Z ) ), member( X,
% 1.28/1.65 intersection( Y, Z ) ) ] )
% 1.28/1.65 , clause( 11223, [ ~( member( X, complement( Y ) ) ), ~( member( X, Y ) ) ]
% 1.28/1.65 )
% 1.28/1.65 , clause( 11224, [ ~( member( X, 'universal_class' ) ), member( X,
% 1.28/1.65 complement( Y ) ), member( X, Y ) ] )
% 1.28/1.65 , clause( 11225, [ =( complement( intersection( complement( X ), complement(
% 1.28/1.65 Y ) ) ), union( X, Y ) ) ] )
% 1.28/1.65 , clause( 11226, [ =( intersection( complement( intersection( X, Y ) ),
% 1.28/1.65 complement( intersection( complement( X ), complement( Y ) ) ) ),
% 1.28/1.65 'symmetric_difference'( X, Y ) ) ] )
% 1.28/1.65 , clause( 11227, [ =( intersection( X, 'cross_product'( Y, Z ) ), restrict(
% 1.28/1.65 X, Y, Z ) ) ] )
% 1.28/1.65 , clause( 11228, [ =( intersection( 'cross_product'( X, Y ), Z ), restrict(
% 1.28/1.65 Z, X, Y ) ) ] )
% 1.28/1.65 , clause( 11229, [ ~( =( restrict( X, singleton( Y ), 'universal_class' ),
% 1.28/1.65 'null_class' ) ), ~( member( Y, 'domain_of'( X ) ) ) ] )
% 1.28/1.65 , clause( 11230, [ ~( member( X, 'universal_class' ) ), =( restrict( Y,
% 1.28/1.65 singleton( X ), 'universal_class' ), 'null_class' ), member( X,
% 1.28/1.65 'domain_of'( Y ) ) ] )
% 1.28/1.65 , clause( 11231, [ subclass( rotate( X ), 'cross_product'( 'cross_product'(
% 1.28/1.65 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.28/1.65 , clause( 11232, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.28/1.65 rotate( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, Z ), X ), T )
% 1.28/1.65 ] )
% 1.28/1.65 , clause( 11233, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.28/1.65 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Z, X ), Y ),
% 1.28/1.65 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.28/1.65 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Z, X )
% 1.28/1.65 , Y ), rotate( T ) ) ] )
% 1.28/1.65 , clause( 11234, [ subclass( flip( X ), 'cross_product'( 'cross_product'(
% 1.28/1.65 'universal_class', 'universal_class' ), 'universal_class' ) ) ] )
% 1.28/1.65 , clause( 11235, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.28/1.65 flip( T ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ), T ) ]
% 1.28/1.65 )
% 1.28/1.65 , clause( 11236, [ ~( member( 'ordered_pair'( 'ordered_pair'( X, Y ), Z ),
% 1.28/1.65 T ) ), ~( member( 'ordered_pair'( 'ordered_pair'( Y, X ), Z ),
% 1.28/1.65 'cross_product'( 'cross_product'( 'universal_class', 'universal_class' )
% 1.28/1.65 , 'universal_class' ) ) ), member( 'ordered_pair'( 'ordered_pair'( Y, X )
% 1.28/1.65 , Z ), flip( T ) ) ] )
% 1.28/1.65 , clause( 11237, [ =( 'domain_of'( flip( 'cross_product'( X,
% 1.28/1.65 'universal_class' ) ) ), inverse( X ) ) ] )
% 1.28/1.65 , clause( 11238, [ =( 'domain_of'( inverse( X ) ), 'range_of'( X ) ) ] )
% 1.28/1.65 , clause( 11239, [ =( first( 'not_subclass_element'( restrict( X, Y,
% 1.28/1.65 singleton( Z ) ), 'null_class' ) ), domain( X, Y, Z ) ) ] )
% 1.28/1.65 , clause( 11240, [ =( second( 'not_subclass_element'( restrict( X,
% 1.28/1.65 singleton( Y ), Z ), 'null_class' ) ), range( X, Y, Z ) ) ] )
% 1.28/1.65 , clause( 11241, [ =( 'range_of'( restrict( X, Y, 'universal_class' ) ),
% 1.28/1.65 image( X, Y ) ) ] )
% 1.28/1.65 , clause( 11242, [ =( union( X, singleton( X ) ), successor( X ) ) ] )
% 1.28/1.65 , clause( 11243, [ subclass( 'successor_relation', 'cross_product'(
% 1.28/1.65 'universal_class', 'universal_class' ) ) ] )
% 1.28/1.65 , clause( 11244, [ ~( member( 'ordered_pair'( X, Y ), 'successor_relation'
% 1.28/1.65 ) ), =( successor( X ), Y ) ] )
% 1.28/1.65 , clause( 11245, [ ~( =( successor( X ), Y ) ), ~( member( 'ordered_pair'(
% 1.28/1.65 X, Y ), 'cross_product'( 'universal_class', 'universal_class' ) ) ),
% 1.28/1.65 member( 'ordered_pair'( X, Y ), 'successor_relation' ) ] )
% 1.28/1.65 , clause( 11246, [ ~( inductive( X ) ), member( 'null_class', X ) ] )
% 1.28/1.65 , clause( 11247, [ ~( inductive( X ) ), subclass( image(
% 1.28/1.65 'successor_relation', X ), X ) ] )
% 1.28/1.65 , clause( 11248, [ ~( member( 'null_class', X ) ), ~( subclass( image(
% 1.28/1.65 'successor_relation', X ), X ) ), inductive( X ) ] )
% 1.28/1.65 , clause( 11249, [ inductive( omega ) ] )
% 1.28/1.65 , clause( 11250, [ ~( inductive( X ) ), subclass( omega, X ) ] )
% 1.28/1.65 , clause( 11251, [ member( omega, 'universal_class' ) ] )
% 1.28/1.65 , clause( 11252, [ =( 'domain_of'( restrict( 'element_relation',
% 1.28/1.65 'universal_class', X ) ), 'sum_class'( X ) ) ] )
% 1.28/1.65 , clause( 11253, [ ~( member( X, 'universal_class' ) ), member( 'sum_class'(
% 1.28/1.65 X ), 'universal_class' ) ] )
% 1.28/1.65 , clause( 11254, [ =( complement( image( 'element_relation', complement( X
% 1.28/1.65 ) ) ), 'power_class'( X ) ) ] )
% 1.28/1.65 , clause( 11255, [ ~( member( X, 'universal_class' ) ), member(
% 1.28/1.65 'power_class'( X ), 'universal_class' ) ] )
% 1.28/1.65 , clause( 11256, [ subclass( compose( X, Y ), 'cross_product'(
% 1.28/1.65 'universal_class', 'universal_class' ) ) ] )
% 1.28/1.65 , clause( 11257, [ ~( member( 'ordered_pair'( X, Y ), compose( Z, T ) ) ),
% 1.28/1.65 member( Y, image( Z, image( T, singleton( X ) ) ) ) ] )
% 1.28/1.65 , clause( 11258, [ ~( member( X, image( Y, image( Z, singleton( T ) ) ) ) )
% 1.28/1.65 , ~( member( 'ordered_pair'( T, X ), 'cross_product'( 'universal_class',
% 1.28/1.65 'universal_class' ) ) ), member( 'ordered_pair'( T, X ), compose( Y, Z )
% 1.28/1.65 ) ] )
% 1.28/1.65 , clause( 11259, [ ~( 'single_valued_class'( X ) ), subclass( compose( X,
% 1.28/1.65 inverse( X ) ), 'identity_relation' ) ] )
% 1.28/1.65 , clause( 11260, [ ~( subclass( compose( X, inverse( X ) ),
% 1.28/1.65 'identity_relation' ) ), 'single_valued_class'( X ) ] )
% 1.28/1.65 , clause( 11261, [ ~( function( X ) ), subclass( X, 'cross_product'(
% 1.28/1.65 'universal_class', 'universal_class' ) ) ] )
% 1.28/1.65 , clause( 11262, [ ~( function( X ) ), subclass( compose( X, inverse( X ) )
% 1.28/1.65 , 'identity_relation' ) ] )
% 1.28/1.65 , clause( 11263, [ ~( subclass( X, 'cross_product'( 'universal_class',
% 1.28/1.65 'universal_class' ) ) ), ~( subclass( compose( X, inverse( X ) ),
% 1.28/1.65 'identity_relation' ) ), function( X ) ] )
% 1.28/1.65 , clause( 11264, [ ~( function( X ) ), ~( member( Y, 'universal_class' ) )
% 1.28/1.65 , member( image( X, Y ), 'universal_class' ) ] )
% 1.28/1.65 , clause( 11265, [ =( X, 'null_class' ), member( regular( X ), X ) ] )
% 1.28/1.65 , clause( 11266, [ =( X, 'null_class' ), =( intersection( X, regular( X ) )
% 1.28/1.65 , 'null_class' ) ] )
% 1.28/1.65 , clause( 11267, [ =( 'sum_class'( image( X, singleton( Y ) ) ), apply( X,
% 1.28/1.65 Y ) ) ] )
% 1.28/1.65 , clause( 11268, [ function( choice ) ] )
% 1.28/1.65 , clause( 11269, [ ~( member( X, 'universal_class' ) ), =( X, 'null_class'
% 1.28/1.65 ), member( apply( choice, X ), X ) ] )
% 1.28/1.65 , clause( 11270, [ ~( 'one_to_one'( X ) ), function( X ) ] )
% 1.28/1.65 , clause( 11271, [ ~( 'one_to_one'( X ) ), function( inverse( X ) ) ] )
% 1.28/1.65 , clause( 11272, [ ~( function( inverse( X ) ) ), ~( function( X ) ),
% 1.28/1.65 'one_to_one'( X ) ] )
% 1.28/1.65 , clause( 11273, [ =( intersection( 'cross_product'( 'universal_class',
% 1.28/1.65 'universal_class' ), intersection( 'cross_product'( 'universal_class',
% 1.28/1.65 'universal_class' ), complement( compose( complement( 'element_relation'
% 1.28/1.65 ), inverse( 'element_relation' ) ) ) ) ), 'subset_relation' ) ] )
% 1.28/1.65 , clause( 11274, [ =( intersection( inverse( 'subset_relation' ),
% 1.28/1.65 'subset_relation' ), 'identity_relation' ) ] )
% 1.28/1.65 , clause( 11275, [ =( complement( 'domain_of'( intersection( X,
% 1.28/1.65 'identity_relation' ) ) ), diagonalise( X ) ) ] )
% 1.28/1.65 , clause( 11276, [ =( intersection( 'domain_of'( X ), diagonalise( compose(
% 1.28/1.65 inverse( 'element_relation' ), X ) ) ), cantor( X ) ) ] )
% 1.28/1.65 , clause( 11277, [ ~( operation( X ) ), function( X ) ] )
% 1.28/1.65 , clause( 11278, [ ~( operation( X ) ), =( 'cross_product'( 'domain_of'(
% 1.28/1.65 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.28/1.65 ] )
% 1.28/1.65 , clause( 11279, [ ~( operation( X ) ), subclass( 'range_of'( X ),
% 1.28/1.65 'domain_of'( 'domain_of'( X ) ) ) ] )
% 1.28/1.65 , clause( 11280, [ ~( function( X ) ), ~( =( 'cross_product'( 'domain_of'(
% 1.28/1.65 'domain_of'( X ) ), 'domain_of'( 'domain_of'( X ) ) ), 'domain_of'( X ) )
% 1.28/1.65 ), ~( subclass( 'range_of'( X ), 'domain_of'( 'domain_of'( X ) ) ) ),
% 1.28/1.65 operation( X ) ] )
% 1.28/1.65 , clause( 11281, [ ~( compatible( X, Y, Z ) ), function( X ) ] )
% 1.28/1.65 , clause( 11282, [ ~( compatible( X, Y, Z ) ), =( 'domain_of'( 'domain_of'(
% 1.28/1.65 Y ) ), 'domain_of'( X ) ) ] )
% 1.28/1.65 , clause( 11283, [ ~( compatible( X, Y, Z ) ), subclass( 'range_of'( X ),
% 1.28/1.65 'domain_of'( 'domain_of'( Z ) ) ) ] )
% 1.28/1.65 , clause( 11284, [ ~( function( X ) ), ~( =( 'domain_of'( 'domain_of'( Y )
% 1.28/1.65 ), 'domain_of'( X ) ) ), ~( subclass( 'range_of'( X ), 'domain_of'(
% 1.28/1.65 'domain_of'( Z ) ) ) ), compatible( X, Y, Z ) ] )
% 1.28/1.65 , clause( 11285, [ ~( homomorphism( X, Y, Z ) ), operation( Y ) ] )
% 1.28/1.65 , clause( 11286, [ ~( homomorphism( X, Y, Z ) ), operation( Z ) ] )
% 1.28/1.65 , clause( 11287, [ ~( homomorphism( X, Y, Z ) ), compatible( X, Y, Z ) ] )
% 1.28/1.65 , clause( 11288, [ ~( homomorphism( X, Y, Z ) ), ~( member( 'ordered_pair'(
% 1.28/1.65 T, U ), 'domain_of'( Y ) ) ), =( apply( Z, 'ordered_pair'( apply( X, T )
% 1.28/1.65 , apply( X, U ) ) ), apply( X, apply( Y, 'ordered_pair'( T, U ) ) ) ) ]
% 1.28/1.65 )
% 1.28/1.65 , clause( 11289, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.28/1.65 Z, X, Y ) ), member( 'ordered_pair'( 'not_homomorphism1'( Z, X, Y ),
% 1.28/1.65 'not_homomorphism2'( Z, X, Y ) ), 'domain_of'( X ) ), homomorphism( Z, X
% 1.28/1.65 , Y ) ] )
% 1.28/1.65 , clause( 11290, [ ~( operation( X ) ), ~( operation( Y ) ), ~( compatible(
% 1.28/1.65 Z, X, Y ) ), ~( =( apply( Y, 'ordered_pair'( apply( Z,
% 1.28/1.65 'not_homomorphism1'( Z, X, Y ) ), apply( Z, 'not_homomorphism2'( Z, X, Y
% 1.28/1.65 ) ) ) ), apply( Z, apply( X, 'ordered_pair'( 'not_homomorphism1'( Z, X,
% 1.28/1.65 Y ), 'not_homomorphism2'( Z, X, Y ) ) ) ) ) ), homomorphism( Z, X, Y ) ]
% 1.28/1.65 )
% 1.28/1.65 , clause( 11291, [ member( y, singleton( x ) ) ] )
% 1.28/1.65 , clause( 11292, [ ~( =( y, x ) ) ] )
% 1.28/1.65 ] ).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 subsumption(
% 1.28/1.65 clause( 4, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.28/1.65 , clause( 11204, [ ~( =( X, Y ) ), subclass( X, Y ) ] )
% 1.28/1.65 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.28/1.65 ), ==>( 1, 1 )] ) ).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 subsumption(
% 1.28/1.65 clause( 5, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y ) ] )
% 1.28/1.65 , clause( 11206, [ ~( subclass( X, Y ) ), ~( subclass( Y, X ) ), =( X, Y )
% 1.28/1.65 ] )
% 1.28/1.65 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.28/1.65 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 subsumption(
% 1.28/1.65 clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X, Z
% 1.28/1.65 ) ] )
% 1.28/1.65 , clause( 11207, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ),
% 1.28/1.65 =( X, Z ) ] )
% 1.28/1.65 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.28/1.65 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 subsumption(
% 1.28/1.65 clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.28/1.65 , clause( 11211, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.28/1.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 subsumption(
% 1.28/1.65 clause( 90, [ member( y, singleton( x ) ) ] )
% 1.28/1.65 , clause( 11291, [ member( y, singleton( x ) ) ] )
% 1.28/1.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 subsumption(
% 1.28/1.65 clause( 91, [ ~( =( y, x ) ) ] )
% 1.28/1.65 , clause( 11292, [ ~( =( y, x ) ) ] )
% 1.28/1.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 factor(
% 1.28/1.65 clause( 11421, [ ~( member( X, 'unordered_pair'( Y, Y ) ) ), =( X, Y ) ] )
% 1.28/1.65 , clause( 6, [ ~( member( X, 'unordered_pair'( Y, Z ) ) ), =( X, Y ), =( X
% 1.28/1.65 , Z ) ] )
% 1.28/1.65 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 paramod(
% 1.28/1.65 clause( 11422, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 1.28/1.65 , clause( 10, [ =( 'unordered_pair'( X, X ), singleton( X ) ) ] )
% 1.28/1.65 , 0, clause( 11421, [ ~( member( X, 'unordered_pair'( Y, Y ) ) ), =( X, Y )
% 1.28/1.65 ] )
% 1.28/1.65 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 1.28/1.65 :=( Y, Y )] )).
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 subsumption(
% 1.28/1.65 clause( 93, [ =( X, Y ), ~( member( X, singleton( Y ) ) ) ] )
% 1.28/1.65 , clause( 11422, [ ~( member( X, singleton( Y ) ) ), =( X, Y ) ] )
% 1.28/1.65 , suCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------